77 ideas
| 23183 | Different abilities are needed for living in an incomplete and undogmatic system [Nietzsche] |
| 23188 | Bad writers use shapeless floating splotches of concepts [Nietzsche] |
| 23212 | A text has many interpretations, but no 'correct' one [Nietzsche] |
| 23199 | What is the search for truth if it isn't moral? [Nietzsche] |
| 23202 | Like all philosophers, I love truth [Nietzsche] |
| 15901 | Trying to represent curves, we study arbitrary functions, leading to the ordinals, which produces set theory [Cantor, by Lavine] |
| 13444 | Cantor's Theorem: for any set x, its power set P(x) has more members than x [Cantor, by Hart,WD] |
| 18098 | Cantor proved that all sets have more subsets than they have members [Cantor, by Bostock] |
| 15505 | If a set is 'a many thought of as one', beginners should protest against singleton sets [Cantor, by Lewis] |
| 10701 | Cantor showed that supposed contradictions in infinity were just a lack of clarity [Cantor, by Potter] |
| 10865 | The continuum is the powerset of the integers, which moves up a level [Cantor, by Clegg] |
| 17832 | Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M] |
| 13016 | The Axiom of Union dates from 1899, and seems fairly obvious [Cantor, by Maddy] |
| 13028 | Replacement was added when some advanced theorems seemed to need it [Zermelo, by Maddy] |
| 14199 | Cantor's sets were just collections, but Dedekind's were containers [Cantor, by Oliver/Smiley] |
| 23196 | Logic is a fiction, which invents the view that one thought causes another [Nietzsche] |
| 10082 | There are infinite sets that are not enumerable [Cantor, by Smith,P] |
| 17626 | The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo] |
| 13483 | Cantor's Paradox: the power set of the universe must be bigger than the universe, yet a subset of it [Cantor, by Hart,WD] |
| 8710 | The powerset of all the cardinal numbers is required to be greater than itself [Cantor, by Friend] |
| 15910 | Cantor named the third realm between the finite and the Absolute the 'transfinite' [Cantor, by Lavine] |
| 23186 | Numbers enable us to manage the world - to the limits of counting [Nietzsche] |
| 15905 | Cantor proved the points on a plane are in one-to-one correspondence to the points on a line [Cantor, by Lavine] |
| 9983 | Cantor took the ordinal numbers to be primary [Cantor, by Tait] |
| 17798 | Cantor presented the totality of natural numbers as finite, not infinite [Cantor, by Mayberry] |
| 9971 | Cantor introduced the distinction between cardinals and ordinals [Cantor, by Tait] |
| 9892 | Cantor showed that ordinals are more basic than cardinals [Cantor, by Dummett] |
| 14136 | A cardinal is an abstraction, from the nature of a set's elements, and from their order [Cantor] |
| 15906 | Cantor tried to prove points on a line matched naturals or reals - but nothing in between [Cantor, by Lavine] |
| 11015 | Cantor's diagonal argument proved you can't list all decimal numbers between 0 and 1 [Cantor, by Read] |
| 15903 | A real is associated with an infinite set of infinite Cauchy sequences of rationals [Cantor, by Lavine] |
| 18251 | Irrational numbers are the limits of Cauchy sequences of rational numbers [Cantor, by Lavine] |
| 15902 | Irrationals and the Dedekind Cut implied infinite classes, but they seemed to have logical difficulties [Cantor, by Lavine] |
| 15908 | It was Cantor's diagonal argument which revealed infinities greater than that of the real numbers [Cantor, by Lavine] |
| 13464 | Cantor proposes that there won't be a potential infinity if there is no actual infinity [Cantor, by Hart,WD] |
| 10112 | The naturals won't map onto the reals, so there are different sizes of infinity [Cantor, by George/Velleman] |
| 8733 | The Continuum Hypothesis says there are no sets between the natural numbers and reals [Cantor, by Shapiro] |
| 17889 | CH: An infinite set of reals corresponds 1-1 either to the naturals or to the reals [Cantor, by Koellner] |
| 13447 | Cantor: there is no size between naturals and reals, or between a set and its power set [Cantor, by Hart,WD] |
| 10883 | Cantor's Continuum Hypothesis says there is a gap between the natural and the real numbers [Cantor, by Horsten] |
| 13528 | Continuum Hypothesis: there are no sets between N and P(N) [Cantor, by Wolf,RS] |
| 9555 | Continuum Hypothesis: no cardinal greater than aleph-null but less than cardinality of the continuum [Cantor, by Chihara] |
| 18174 | Cantor extended ordinals into the transfinite, and they can thus measure infinite cardinalities [Cantor, by Maddy] |
| 15893 | Cantor's theory concerns collections which can be counted, using the ordinals [Cantor, by Lavine] |
| 18173 | Cardinality strictly concerns one-one correspondence, to test infinite sameness of size [Cantor, by Maddy] |
| 10232 | Property extensions outstrip objects, so shortage of objects caused the Caesar problem [Cantor, by Shapiro] |
| 18176 | Pure mathematics is pure set theory [Cantor] |
| 8631 | Cantor says that maths originates only by abstraction from objects [Cantor, by Frege] |
| 23211 | Events are just interpretations of groups of appearances [Nietzsche] |
| 23201 | The 'I' does not think; it is a construction of thinking, like other useful abstractions [Nietzsche] |
| 23207 | Appearance is the sole reality of things, to which all predicates refer [Nietzsche] |
| 23197 | Memory is essential, and is only possible by means of abbreviation signs [Nietzsche] |
| 23206 | Schematic minds think thoughts are truer if they slot into a scheme [Nietzsche] |
| 23209 | Each of our personal drives has its own perspective [Nietzsche] |
| 23184 | The mind is a simplifying apparatus [Nietzsche] |
| 23190 | Consciousness is our awareness of our own mental life [Nietzsche] |
| 23191 | Minds have an excluding drive to scare things off, and a selecting one to filter facts [Nietzsche] |
| 23213 | The greatest drive of life is to discharge strength, rather than preservation [Nietzsche] |
| 23210 | That all events are necessary does not mean they are compelled [Nietzsche] |
| 23189 | Concepts are rough groups of simultaneous sensations [Nietzsche] |
| 23192 | Concepts don’t match one thing, but many things a little bit [Nietzsche] |
| 8715 | Infinities expand the bounds of the conceivable; we explore concepts to explore conceivability [Cantor, by Friend] |
| 23187 | Whatever their origin, concepts survive by being useful [Nietzsche] |
| 13454 | Cantor says (vaguely) that we abstract numbers from equal sized sets [Hart,WD on Cantor] |
| 23205 | Thought starts as ambiguity, in need of interpretation and narrowing [Nietzsche] |
| 23198 | Aesthetics can be more basic than morality, in our pleasure in certain patterns of experience [Nietzsche] |
| 23208 | Caesar and Napoleon point to the future, when they pursue their task regardless of human sacrifice [Nietzsche] |
| 23193 | Napoleon was very focused, and rightly ignored compassion [Nietzsche] |
| 23214 | For the strongest people, nihilism gives you wings! [Nietzsche] |
| 23203 | The great question is approaching, of how to govern the earth as a whole [Nietzsche] |
| 23200 | The controlling morality of aristocracy is the desire to resemble their ancestors [Nietzsche] |
| 23194 | People feel united as a nation by one language, but then want a common ancestry and history [Nietzsche] |
| 23204 | To be someone you need property, and wanting more is healthy [Nietzsche] |
| 23195 | Laws of nature are actually formulas of power relations [Nietzsche] |
| 10863 | Cantor proved that three dimensions have the same number of points as one dimension [Cantor, by Clegg] |
| 23185 | In chemistry every substance pushes, and thus creates new substances [Nietzsche] |
| 13465 | Only God is absolutely infinite [Cantor, by Hart,WD] |